Aides from both parties tell CNN talks on trying to reach a deficit reduction agreement are essentially over.

Story highlights

A prayer vigil is held near the White House; others are scheduled in cities this week

The deficit reduction committee has until Wednesday to reach a deal on $1.2 trillion in savings

Its first deadline is Monday

If the committee fails, across-the-board cuts will follow

Members of the "super committee" charged with coming up with $1.2 trillion in budget cuts are focused on how to announce failure to reach a deal, Democratic and Republican aides confirmed to CNN Sunday.

While aides said no final decision had been made, they acknowledged that -- barring an unforeseen development -- an announcement of an end to negotiations is the most likely scenario.

Talks on trying to reach a deficit reduction agreement are essentially over, and discussions are focused on a Monday announcement, a senior Democratic aide said.

Another senior Democratic source said, "No decisions or agreement has been reached concerning any announcement or how this will end. But, yes, the likely outcome is no agreement will be reached." A Republican aide said, "I don't think they've decided when they will do it."

Members of the 12-member bipartisan debt committee said Sunday a wide chasm remains.

A late Monday deadline looms for some kind of plan to move forward, with a vote required by Wednesday.

The mood on the morning news shows was somber, with just a glimmer of hope.

"I'm going to be waiting all day," Washington Sen. Patty Murray, Democratic co-chair of the committee told CNN's Candy Crowley on "State of the Union."

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"I'll be at the table, as I've been, willing to talk to any Republican who says, look, my country is more important, this pile of bills is not going to go away, the challenges that we have is not going to disappear. We need to cross that divide," said Murray.

Her Republican counterpart, Rep. Jeb Hensarling of Texas, said "nobody wants to give up hope."

"Reality is to some extent starting to overtake hope," Hensarling told "Fox News Sunday." But there were 12 good people who invested a lot in this trying to find common ground to try to achieve the goal of this committee."

Murray took harsh aim at Republicans who took a pledge not to raise taxes created by the president of the conservative group Americans for Tax Reform.

"I'll tell you one of the problems has been a pledge that too many Republicans took to a Republican wealthy lobbyist by the name of Grover Norquist, whose name has come up in meetings time and time again," Murray said, adding she was optimistic a compromise would be reached.

Sen. Pat Toomey, R-Pennsylvania, said things weren't looking good for a deal.

"There is still an opportunity. There's a plan on the table that would at least take us halfway to our goal," he told CBS' "Face the Nation."

Sen. Jon Kyl, R-Arizona, reiterated the GOP mantra that Bush-era tax cuts should continue and entitlement spending be cut. Democrats are keen on letting the Bush-era cuts expire for the highest-income Americans in 2012.

"In Washington, there are folks who won't cut a dollar unless we raise taxes," he said on NBC's "Meet the Press."

"If you want to get serious about the deficit our country has to grow economically," Kyl said. "You can't grow if you raise taxes in the middle of a recession."

Meanwhile, an interfaith group held a prayer vigil Sunday in Lafayette Park near the White House to urge Congress not to make budget cuts that would likely impact the poor.

"We gather this time with an audacious purpose and that is to ask God ... to move the hearts of policy makers that they will act and make decisions with compassion and fairness," the Rev. Dr. Michael Kinnamon, general secretary of the National Council of the Churches of Christ, said in leading the crowd in prayer.

Similar vigils will be held this week in Los Angeles; Richmond, Virginia; Philadelphia and Dallas.

While the 12-member panel's deadline for a final vote is Wednesday, any blueprint must be made available 48 hours in advance of a committee vote and must be accompanied by a Congressional Budget Office analysis scoring how much it would reduce deficits.

To stave off automatic spending cuts known as a sequester, the super committee must propose ways to reduce deficits by at least $1.2 trillion over 10 years. At least seven of its 12 members must approve a plan in order to send it to the House and Senate in the form of legislation.

Then, both chambers must vote on the bill, without amendment, by December 23. For the plan to pass, a simple majority in each chamber must vote in favor.

A failure to pass any agreement would result in $1.2 trillion in automatic spending cuts across much of the federal budget starting in 2013, evenly divided between defense and non-defense spending. Defense Secretary Leon Panetta warned Congress this week that such cuts could cripple the American military establishment.

Since Congress made the law governing the sequester, it can also amend or repeal it, as some lawmakers are pushing for.

Rep. Xavier Becerra, a Democrat from California, said Sunday the challenge of reaching an agreement would require putting aside egos and special interest pledges.

"None of the 12 of us took this job so we could end up with sequester," Becerra told CNN after appearing on the Fox News program. "I was always taught when you play a sport you don't give up until the buzzer sounds and there's still time on the clock. It's too early to talk about failure."

While Democrats have expressed concern about deep cuts in social spending, programs such as Social Security, Medicaid, food stamps and veterans' benefits would be spared the budget ax.

On Friday, Republicans floated a $640 billion package, including roughly $540 billion in savings and fees, that would allow negotiators to claim at least partial success and hold down the amount of the automatic cuts.

The plan features mandatory spending cuts and some revenue from closing one tax loophole for corporate jet owners, along with some government fees. This would only address about half of the super committee's mandate to cut at least $1.2 trillion.

Key Republicans broke with their party's anti-tax orthodoxy this week with news of a proposal by Toomey that includes $400 billion in increased revenue, including tax hikes.

Toomey's plan would lower overall tax rates while limiting tax breaks in a way that would raise $250 billion. Republicans estimate that the reform would lead to economic growth generating another $110 billion. A change in how tax brackets are adjusted for inflation would raise another $40 billion.

The plan also includes $800 billion in spending cuts, thereby hitting the minimum threshold of $1.2 trillion in deficit reduction.

Democrats have proposed a solution that would generate $400 billion from increased tax collections and $700 billion in spending meant to jump-start the economy, including an extension of the payroll tax cut, extended unemployment benefit payments and money to permanently prevent cuts in payments to doctors who treat Medicare patients.

Democrats want to offset those costs with money saved from winding down the wars in Iraq and Afghanistan, a move some legislators in both parties characterize as an accounting gimmick.